Results 11 to 20 of about 680,985 (272)
Combinatorial Hopf Algebras of Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra.
Carolina Benedetti +2 more
doaj +3 more sources
Rota–Baxter (Co)algebra Equation Systems and Rota–Baxter Hopf Algebras [PDF]
Mathematics, 2022 We introduce and discuss the notions of Rota–Baxter bialgebra equation systems and Rota–Baxter Hopf algebras. Then we construct a lot of examples based on Hopf quasigroups.
Yue Gu, Shuanhong Wang, Tianshui Ma
doaj +2 more sources
Interacting Hopf Algebras [PDF]
Journal of Pure and Applied Algebra, 2014 We introduce the theory IHR of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IHR are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four ...
F. Bonchi, P. Sobocinski, F. Zanasi
semanticscholar +8 more sources
Cobraided smash product Hom-Hopf algebras [PDF]
, 2014 Let $(A,\a)$ and $(B,\b)$ be two Hom-Hopf algebras. In this paper, we construct a class of new Hom-Hopf algebras: $R$-smash product $(A\natural_R B,\a\o \b)$.
Tianshui Ma, Haiying Li, Tao Yang
openalex +3 more sources
A note on the Zariski lemma for Hopf algebras
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2004 The formulation of the lemma of Zariski is given for coactions of a class of Hopf algebras of the additive group on algebras. Known formulations and consequences of the lemma of Zariski for derivations and differentiations are revised.
Utano, R, Restuccia, G
doaj +3 more sources
Ann Comb, 2022 AbstractIn this paper, we expand on the notion of combinatorial presheaf, first introduced explicitly by Aguiar and Mahajan in 2010 but already present in the literature in some other points of view. We do this by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we consider functions that count the
Penaguiao R.
europepmc +5 more sources
Advances in Mathematics, 2014 Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees.
G. Châtel, Vincent Pilaud
semanticscholar +4 more sources
On the Structure of Hopf Algebras
The Annals of Mathematics, 1965 induced by the product M x M e M. The structure theorem of Hopf concerning such algebras has been generalized by Borel, Leray, and others. This paper gives a comprehensive treatment of Hopf algebras and some surrounding topics.
J. Milnor, John C. Moore
semanticscholar +4 more sources
Post-Hopf algebras, relative Rota--Baxter operators and solutions to the Yang--Baxter equation [PDF]
Journal of Noncommutative Geometry, 2022 In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra.
Yunnan Li, Y. Sheng, Rong Tang
semanticscholar +1 more source
Amplitudes, Hopf algebras and the colour-kinematics duality [PDF]
Journal of High Energy Physics, 2022 It was recently proposed that the kinematic algebra featuring in the colour-kinematics duality for scattering amplitudes in heavy-mass effective field theory (HEFT) and Yang-Mills theory is a quasi-shuffle Hopf algebra.
A. Brandhuber +5 more
semanticscholar +1 more source